A Filter-Based Approach for Approximate Circular Pattern Matching

Azim, Md. Aashikur Rahman; Iliopoulos, Costas S.; Rahman, M. Sohel; Samiruzzaman, M.

doi:10.1007/978-3-319-19048-8_3

Cited by 4 publications

(2 citation statements)

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“…In many real-world applications, such as in bioinformatics [4,22,25,7] or in image processing [3,33,34,32], any cyclic shift (rotation) of P is a relevant pattern, and thus one is interested in computing the minimal distance of every length-m substring of T and any cyclic shift of P , if this distance is no more than k. This is the circular pattern matching with k mismatches (k-CPM) problem. A multitude of papers [17,8,6,5,9,24] have thus been devoted to solving the k-CPM problem but, to the best of our knowledge, only average-case upper bounds are known; i.e. in these works the assumption is that text T is uniformly random.…”

Section: Introductionmentioning

confidence: 99%

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Circular Pattern Matching with k Mismatches

Charalampopoulos

Kociumaka

Pissis

et al. 2019

Fundamentals of Computation Theory

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The k-mismatch problem consists in computing the Hamming distance between a pattern P of length m and every length-m substring of a text T of length n, if this distance is no more than k. In many real-world applications, any cyclic shift of P is a relevant pattern, and thus one is interested in computing the minimal distance of every length-m substring of T and any cyclic shift of P . This is the circular pattern matching with k mismatches (k-CPM) problem. A multitude of papers have been devoted to solving this problem but, to the best of our knowledge, only average-case upper bounds are known. In this paper, we present the first non-trivial worst-case upper bounds for the k-CPM problem. Specifically, we show an O(nk)-time algorithm and an O(n + n m k 5 )-time algorithm. The latter algorithm applies in an extended way a technique that was very recently developed for the k-mismatch problem [Bringmann et al., SODA 2019].

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Section: Introductionmentioning

confidence: 99%

“…A 1-occurrence of P = aabbbb in text T = aaccbbxbaaab at position p = 4 with rotation x = 2; M (4, 2) = {(4, 2), (5, 3), (6, 4),(7,5), (8, 0), (9, 1)}.…”

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confidence: 99%